26.10.17 problem Exercise 35.17, page 504

Internal problem ID [7146]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.17, page 504
Date solved : Tuesday, September 30, 2025 at 04:23:19 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&=y^{\prime } {\mathrm e}^{y} \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=0 \\ y^{\prime }\left (3\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.099 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x) = diff(y(x),x)*exp(y(x)); 
ic:=[y(3) = 0, D(y)(3) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\ln \left (-x +4\right ) \]

✓ Mathematica. Time used: 5.97 (sec). Leaf size: 13

ode=D[y[x],{x,2}]==D[y[x],x]*Exp[y[x]]; 
ic={y[3]==0,Derivative[1][y][3 ]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\log (4-x) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(y(x))*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(3): 0, Subs(Derivative(y(x), x), x, 3): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - exp(-y(x))*Derivative(y(x), (x, 2)) cannot be solved by the factorable group method